Related papers: Fractonic Chern-Simons and BF theories
We propose a fermion Chern-Simons field theory describing two- dimensional electrons in the lowest Landau level. This theory is constructed with a complete set of states, and the lowest Landau level constraint is enforced through a…
The discovery of zero-field fractional Chern insulators (FCIs) in moir\'e materials has attracted intense interest in the interplay between topology and correlations. Here, we demonstrate that fractionalized topological order can emerge…
There is exactly one bosonic (3+1)-dimensional topological order whose only nontrivial particle is an emergent boson: pure $\mathbb{Z}_2$ gauge theory. There are exactly two (3+1)-dimensional topological orders whose only nontrivial…
We investigate (3+1)d topological orders in fermionic systems with an anomalous $\mathbb{Z}_{2N}^{\mathrm{F}}$ symmetry, where its $\mathbb{Z}_2^{\mathrm{F}}$ subgroup is the fermion parity. Such an anomalous symmetry arises as the discrete…
We describe topologically ordered and fracton ordered states on novel geometries which do not have an underlying manifold structure. Using tree graphs such as the $k$-coordinated Bethe lattice ${\cal B}(k)$ and a hypertree called the…
We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple one by taking its semi-direct product with its Lie algebra. We find that the standard knot…
The Chern-Simons (CS) theory in three dimensions with a compact gauge group G is studied. Starting from the BRST quantization of the theory defined in R^3, the values of gauge invariants observables are computed in any closed and orientable…
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…
Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of…
It has been conjectured that 3d fermions minimally coupled to Chern-Simons gauge fields are dual to 3d critical scalars, also minimally coupled to Chern-Simons gauge fields. The large $N$ arguments for this duality can formally be used to…
We begin with an introduction to topological order using Wegner's quantum $Z_2$ gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying $Z_2$ magnetic flux. The interplay between…
This is intended as a broad introduction to Chern-Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system --with a fiber bundle formulation-- in more than three dimensions,…
We study the relation between the frame-like and metric-like formulation of higher-spin gauge theories in three space-time dimensions. We concentrate on the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the frame-like…
Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry…
In the Maxwell--Chern-Simons theory coupled to $N_f$ flavors of 4-component fermions (or even number of 2-component fermions) we construct the gauge-covariant effective potential written in terms of two order parameters which are able to…
We present a theoretical framework for a class of generalized $U(1)$ gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then…
Gravitational anomalies can be realized on the boundary of topologically ordered states in one higher dimension and are described by topological orders in one higher dimension. In this paper, we try to develop a general theory for both…
The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in three dimensions induces…
We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual…
A theoretical description is presented for low-temperature magnetic-field induced three-dimensional (3D) ordering transitions in strongly anisotropic quantum antiferromagnets, consisting of weakly coupled antiferromagnetic spin-1/2 chains…